Mathematics High School

The function f ( x ) = 2 x ^2 − x − 4 models the shape of a ditch. What is the average slope over the interval −4 ≤ x ≤ 2?

Answers

Answer 1

Answer:

[tex]Rate = -5[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 2x^2 - x - 4[/tex]

[tex]-4 \le x \le 2[/tex]

Required

Determine the average slope over the given interval

This is calculated as:

[tex]Rate= \frac{f(b) - f(a)}{b - a}[/tex]

Where:

[tex]a = -4[/tex]

[tex]b =2[/tex]

So:

[tex]Rate= \frac{f(2) - f(-4)}{2 - (-4)}[/tex]

[tex]Rate= \frac{f(2) - f(-4)}{2 +4}[/tex]

[tex]Rate= \frac{f(2) - f(-4)}{6}[/tex]

Solving for f(2) and f(-4), we have:

[tex]f(x) = 2x^2 - x - 4[/tex]

[tex]f(2) = 2 *2^2 -2 - 4[/tex]

[tex]f(2) = 2[/tex]

[tex]f(-4) = 2*(-4)^2 - (-4) - 4[/tex]

[tex]f(-4) = 2*16 +4 - 4[/tex]

[tex]f(-4) = 32[/tex]

So, the equation becomes

[tex]Rate= \frac{f(2) - f(-4)}{6}[/tex]

[tex]Rate= \frac{2 - 32}{6}[/tex]

[tex]Rate= \frac{-30}{6}[/tex]

[tex]Rate = -5[/tex]

Related Questions

What happens to the value of the expression b-1b−1b, minus, 1 as bbb increases?

Answers

Answer:

the answer is A It increases.

that's the right answer go add me snap cutegirllove17

Step-by-step explanation:

have a good day

Please help me solve 8n+2-6n-13=9+2n-13

Answers

no solution since the 2n on both sides cross out

Answer:

It has no solution, unless there's a specific way it needs to be solved

Step-by-step explanation:

Can someone help me please????

Answers

i think it would be the last one sorry if i’m wrong

Help! Will mark brainliest

Answers

Answer:

x < −4

Step-by-step explanation:

hope this helps u with ur question lol

A number when divided by 5 gives 0 as remainder, that number when divided by 7 gives 0 as remainder also. What will be the remainder when that number is divided by 35?

Answers

Answer:

zero

Step-by-step explanation:

The computation of the remainder when the number would be divided by 35

Let the number be x

So if x is divided by 5 gives the remainder 0

x = 0

And, if x is divided by 7 gives the remainder 0

x = 0

So if x is divided by 35 so the remainder is also zero

Need help with all three ​

Answers

Answer:

7. 3000

8. 768

9. 378

Step-by-step explanation:

7. 60×50=3000

8. 48×16=768

9. 21×18=378

PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer: D 12

Step-by-step explanation:

A meteorologist reports that the chance of snow is less than 30%. The correct inequality to represent this comparison is s < 30. The variable s represents the likelihood of snow.

Which numbers are solutions of the inequality?
Choose all that apply.
20%
35%
17%
30%
29 and one-half percent%
1.5%

Answers

The equation is less than 30 so any number smaller than 30 are correct.

Answers: 20%, 17%, 1.5%

Answer:

The equation is less than 30 so any number smaller than 30 are correct.  

Answers: 20%, 17%, 1.5% 29 1/2%

Step-by-step explanation:

H+ ions increase in concentration at lower pH values. Calculate how many more H+ ions there are in a solution at a pH = 2 than in a solution at a pH = 6. Find the concentration of H+ ions at a pH = 2 and at a pH = 6 in Table B. Then divide the concentration of H+ ions at a
pH = 2 by the of H+ ions at a pH = 6. Record your answer in Table C.

What is the concentration of H+ ions at a pH = 2?

mol/L

What is the concentration of H+ ions at a pH = 6?

mol/L

How many more H+ ions are there in a solution at a
pH = 2 than in a solution at a pH = 6?

Answers

Answer:

What is the concentration of H+ ions at a pH = 2?

⇒ 0.01 mol/L

What is the concentration of H+ ions at a pH = 6?

⇒ 0.000001 mol/L

How many more H+ ions are there in a solution at a

pH = 2 than in a solution at a pH = 6?

⇒ 10,000

Step-by-step explanation:

Answer:

What is the concentration of H+ ions at a pH = 2?

0.01

 

What is the concentration of H+ ions at a pH = 6?

0.000001

 

How many more H+ ions are there in a solution at a

pH = 2 than in a solution at a pH = 6?

10,000

Step-by-step explanation:

skracanie ułamków

224/100 =
308/100 =
125/1000=
444\1000 =

Answers

Answer:

224/100 = 2 24/100

= 2 6/25

308/100 = 3 8/100

= 3 2/25

125/1000 = ⅛

444/1000 = 111/250

Can someone plz help me! Thx!

Answers

Answer:

q

Step-by-step explanation:

a

Answer:

Step-by-step explanation:

Work out ( 6x10^2) divide by (3x10^-5)
Give your answer in standard form.

Answers

2•10^7 that’s the answer hope it helps

PLEASE HELP MATHS
What is the domain of the function y= 3 In x graphed below​

Answers

Answer:

This question makes no sense

Step-by-step explanation:

The domain is all real x btw

the ratio of two number is 7 to 3 and their sum is 50 find the two number​

Answers

Answer:

35:15

Step-by-step explanation:

7:3=10 (7+3)

14:6=20 (14+6)

21:9=30 (21+9)

28:12=40 (28+12)

35:15=50 (35+15)

There is a more mathematical way to solve this but it isn't coming to mind rn so

The circumference of a circle is m. What is the area , in square meters ? Express your answer in terms of pi

Answers

Answer:

area = m²/2π

Step-by-step explanation:

∵ circumference of circle = 2πr = m

∴ r = m/2π

∵ area of circle = πr²

∴ area of circle = (m/2π)² × π = m²/2π² × π = m²/2π

hope this helps

Erin buys a bag of peanuts that weighs 3/4 of a pound later that week the bag is 2/3 full how much dose the bag of panuts wiegh now

Answers

Answer:

1 ÷ 2 pounds

Step-by-step explanation:

The computation is shown below:

As we know that

1 pound = 0.454 Kg

Peanut starting weight = 3 ÷ 4 of a pound.

In the case when  the bag is 2/3 full, so the weight is  

= 2 ÷ 3 × 3 ÷ 4

= 1 ÷ 2 pounds

What is the factorization of the trinomial below?
-2x^3-10x^2-12x

Answers

Answer: -2x (x+3) (x+2)

Step-by-step explanation:

Answer:

(−2x)(x+2)(x+3)

Step-by-step explanation:

−2x3−10x2−12x

=(−2x)(x+2)(x+3)

Answer:

(−2x)(x+2)(x+3)

Can someone tell me if this is right?

Answers

Answer:

Step-by-step explanation:

You have shaded 4/7=8/14

6/7=12/14

So you need to shade 12 boxes

PLEASE HELP WILL MARK YOU BRAINLIEST!! HOW DO YOU SOLVE 22 = -11k

Answers

22=-11k is K= -2 hope this helps
K=-2

1st: swap the side move 22 to the right side and -11k to the left.
2nd: divide both sides by -11k
3rd: k=-2

help me solve for x ?

Answers

the answer would be x=12

Answer:

x = 12

Step-by-step explanation:

[tex](4x - 5) \degree +(3x + 11) \degree = 90\degree \\(complementary \: \angle s) \\ \\ (4x - 5 + 3x + 11)\degree = 90\degree \\ \\ (7x + 6)\degree = 90\degree \\ \\ 7x + 6 = 90 \\ \\ 7x = 90 - 6 \\ 7x = 84 \\ \\ x = \frac{84}{7} \\ \\ x = 12[/tex]

The coordinates of the vertices of a triangle are A( 2,3) , B ( 9,1) , C ( 12,14) Suppose each coordinate is multiplied by 3. What is the perimeter of this triangle?







Answers

9514 1404 393

Answer:

  about 106.5 units

Step-by-step explanation:

The length of each side is found using the distance formula:

  d = √((x2-x1)^2 +(y2-y1)^2)

For example, the length of side AB is ...

  d = √((9 -2)^2 +(1 -3)^2) = √(7^2 +(-2)^2) = √53 ≈ 7.28

The other side lengths are calculated the same way. The sum of side lengths of the given triangle is ...

  AB +BC +CA = 7.28 +13.34 +14.87 = 35.49

__

Multiplying each coordinate by 3 effectively dilates the triangle by a factor of 3 about the origin. That increases the perimeter by a factor of 3, so it is ...

  3(35.49) ≈ 106.5 . . . . units

_____

I find it convenient to use a calculator or spreadsheet to do the tedious calculations.

If the edge length of a cube is 13 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points)

Answers

Answer:

take side as a

volume of cube=a×a×a

= 13×13×13

(im so sorry if im wrong)

Please help me with the question please ASAP ASAP I’m begging please

Answers

Answer: a= 144. b= 67

Step-by-step explanation:

Angle b and the angle of measure 113 are same side interior angles which sum to 180 (When 2 parallel lines are cut by a transversal, special angles are formed)

113+b=180. Subtract 113 from both sides.

b= 67 degrees

Now that you have b, the interior angles of four sided figures sum to 360.

a+113+67+36=360. Combine like terms.

a+216=360. Subtract 216 from both sides.

a= 144 degrees

Multi answer inequality! Please help and comment only if you know!

Answers

Answer:

-8, 0, and -12

Step-by-step explanation:

Using -7 would get you 8. Using -5 would get you 4

slope = -3; y-intercept = 2

Answers

Answer:

y= -3x+2

Step-by-step explanation:

Help me please !!!!! I need help

Answers

10 percent of 300 is 30

3 hours and 10 minutes =190

please help me with this question

Answers

Answer:

The third equation

PLSSSSSSS HELPPPP ASAPPPP

Answers

Answer:

b

Step-by-step explanation:

figure 1 is maped to figure 2. check the difference

Bethany bought a box of markers. She gave 6 to her friend. If Bethany now has 52 markers, how many markers were in the box she bought?

Answers

Answer:

58 markers

Step-by-step explanation:

52 + 6 = 58

Answer:

58 markers

Step-by-step explanation:

x-6=52 Set up the problem. "x" represents the number of markers.

 +6 +6 Add 6 to both sides to isolate x

x    =58

Ahmed owns a land of breadth (x+7) units &having an area of 2+ 14x + 49 sq. Units. (i)Find its length.

Answers

Answer:

l = (x+7) units

Step-by-step explanation:

Given that,

Breadth of the rectangle, b = (x+7) units

Area of the rectangle, [tex]A=x^2+14x+49[/tex]

The area of a rectangle is given by :

[tex]A=lb\\\\l=\dfrac{A}{b}\\\\l=\dfrac{(x^2+14x+49)}{(x+7)}\\\\l=\dfrac{(x+7)^2}{(x+7)}\\\\l=(x+7)\ \text{units}[/tex]

So, the length of the land is (x+7) units.

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